Precise Coulomb wave functions for a wide range of complex l, eta and z

Abstract A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the Schrodinger equation in order to provide very stable calculations, even for large values of | η | or | ℑ ( l ) | . Moreover, a simple analytic continuation for R ( z ) 0 is introduced, so that this zone of the complex z-plane does not pose any problem. This code is particularly well suited for low-energy calculations and the calculation of resonances with extremely small widths. Numerical instabilities appear, however, when both | η | and | ℑ ( l ) | are large and | R ( l ) | comparable or smaller than | ℑ ( l ) | . Program summary Title of program: cwfcomplex Catalogue number:ADYO_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYO_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers on which the program has been tested: DELL GX400 Operating systems: Linux, Windows Programming language used: C++ No. of bits in a word: 64 No. of processors used: 1 Has the code been vectorized?: no No. of bytes in distributed program, including test data, etc.: 33 092 No. of lines in distributed program, including test data, etc.: 3210 Distribution format:tar.gz Nature of physical problem: The calculation of Coulomb wave functions with all of their arguments complex is revisited. The new methods introduced allow to greatly augment the range of accessible l, η, and z. Method of solution: Power/asymptotic series and continued fractions are supplemented with direct integrations of the Coulomb Schrodinger equation. Analytic continuation for R ( z ) 0 is also precisely computed using linear combinations of the functions provided by standard methods, which do not follow the branch cut requirements demanded for Coulomb wave functions. Typical running time: N/A Unusual features of the program: none